In Fig. REF , we show the Bloch (gray) and non-Bloch (black) winding numbers. The non-Bloch winding number is quantized to integers, and changes its value at topological transitions that are consistent with the gap-closing points in Fig. REF . By contrast, the Bloch winding number can take half-integer values, and it does not indicate the topological transitions of the system under the open boundary condition. Note that half-integer winding numbers have previously been reported in the non-Hermitian, asymmetric Su-Schrieffer-Heeger model [1]}, [2]}, where explicit geometric interpretations can be found based on its chiral symmetry. While chiral symmetry is absent in our model, the origin of these half-integer winding numbers, and their general relation to the non-Hermitian skin effect, are interesting open questions.
